Making sense of eagles vs. turbines

So earlier this week, when I read that officials of a wind power company had asked for a permit that would allow the company's wind turbines to kill a given number of golden eagles each year, I became concerned.

Bald and golden eagles are protected under the Bald and Golden Eagle Protection Act of 1940. It struck me as odd that representatives of a "green" industry would ask permission to violate that law a few times a year.

I certainly understand why: If the feds allow the company's turbines to kill some eagles, the feds then can't shut the company down unless the number killed exceeds the allowable limit. In other words, the company gets some leeway it otherwise might not get.

Wind turbine towers stand 200 to 300 feet tall, and their blades range from 100 to 150 feet in length. The blades rotate 10 to 22 times each minute.

Let's split the difference between the industry minimums and maximums and assume a turbine blade length of 125 feet. Double that to get the diameter of the circle the rotor tips describe, and multiply by pi (3.14159265359 ... OK, I'm a geek) to find out how far each blade tip travels per revolution. Answer: 785.39 feet.

Split the difference between minimum and maximum rotation rates to get an average rotation rate of 16 rpm. So each blade makes a complete circle in 3.75 seconds.

If that still seems pretty slow, divide the distance traveled (735.39 feet) by the elapsed time (3.75 seconds). Answer: 196.1 feet per second. Since 1 foot per second equals (geek alert!) 0.681818182 miles an hour, those blades are cookin' along at 133.705 miles an hour!

According to a 1984 article in the journal Nature, the mean startle response time (recognition plus start of action) for birds is roughly 105 milliseconds - a shade more than a tenth of a second. So any eagle less than 175.5 feet away when it saw an onrushing blade would have no chance at all to react by the time it was hit.

Now consider that each turbine has three blades. That means a blade comes whizzing past a given spot every 1.25 seconds (3.75 seconds per revolution per blade, divided by three blades). That means an eagle would have just 1.145 seconds to take evasive action (1.25 seconds between blades, minus 0.105 seconds reaction time) even if it saw the danger coming.

Even for the most nimble eagle, that's not much time.

Wind farms are usually located on ridges. Eagles tend to use ridgelines as migration routes. Our example turbine has blades that cover a patch of sky 1.146 acres in size (Area of a circle = pi times the radius squared; in this case, 3.14159 times 125 times 125. Answer is in square feet. Divide by 43,560 square feet per acre to calculate the acreage).

There are often 20 or more turbines in a single wind farm. String them along a ridge, and you've strung up a pretty formidable gantlet for an eagle to run.

Should anyone assume from the preceding paragraphs that I'm opposed to wind farms, please rest assured that I am not. On balance, they probably help the environment more than they harm it.

I did the math simply to satisfy my own curiosity. I've seen how slowly wind turbine blades appeared to turn and wondered how eagles could ever fall victim to them. Now I understand.